Question

Simplify the following rational expression: x^2-9/x+2 divided by x-3/x^2-4.

Answer 1

Interpret the expression as ((x^2 − 9)/(x + 2)) ÷ ((x − 3)/(x^2 − 4)).

Factor and invert the divisor:
((x − 3)(x + 3)/(x + 2)) * ((x^2 − 4)/(x − 3))
= ((x − 3)(x + 3)/(x + 2)) * ((x − 2)(x + 2)/(x − 3))

Cancel (x − 3) and (x + 2):
= (x + 3)(x − 2) = x^2 + x − 6.

Restrictions from the original expression: x ≠ −2, 2, 3. (The simplified polynomial equals x^2 + x − 6 for all other x.)